A strength inversion origin for non-volcanic tremor

Non-volcanic tremor is a particularly enigmatic form of seismic activity. In its most studied subduction zone setting, tremor typically occurs within the plate interface at or near the shallow and deep edges of the interseismically locked zone. Detailed seismic observations have shown that tremor is composed of repeating small low-frequency earthquakes, often accompanied by very-low-frequency earthquakes, all involving shear failure and slip. However, low-frequency earthquakes and very-low-frequency earthquakes within each cluster show nearly constant source durations for all observed magnitudes, which implies characteristic tremor sub-event sources of near-constant size. Here we integrate geological observations and geomechanical lab measurements on heterogeneous rock assemblages representative of the shallow tremor region offshore the Middle America Trench with numerical simulations to demonstrate that these tremor events are consistent with the seismic failure of relatively weaker blocks within a stronger matrix. In these subducting rocks, hydrothermalism has led to a strength-inversion from a weak matrix with relatively stronger blocks to a stronger matrix with embedded relatively weaker blocks. Tremor naturally occurs as the now-weaker blocks fail seismically while their surrounding matrix has not yet reached a state of general seismic failure.


Toughness
Energy that can be absorbed (per unit volume) by a material prior to its failure Measure of the body's resistance to failure by fracture when a body is stressed

Supplementary Information on the Osa Melange
The section of the Osa Melange outcropping in the northwest part of the Osa Peninsula is known as the San Pedrillo Unit (Buchs et al., 2009;Clarke et al., 2018;Di Marco et al., 1995;Vannucchi et al., 2006). This unit represents the oldest member of the Osa Melange with depositional ages from the Campanian to the middle Eocene(Di Marco et al., 1995), while its involvement in the subduction zone deformation is tentatively dated to the late Oligocene-early Miocene (Vannucchi et al., 2006). The San Pedrillo Unit is composed of a volcanoclastic greywacke matrix containing blocks of basalt, gabbro, turbidites, hemi-pelagic and pelagic sediments, and subordinate dolerite (Buchs et al., 2009;Clarke et al., 2018;Meschede et al., 1999;Vannucchi et al., 2006). Both the blocks and the matrix show widespread, but not uniform low-grade metamorphic alteration with hydrous minerals precipitation not exceeding the prehnite-pumpellyite facies (SM Figure 1) (Buchs et al., 2009;Meschede et al., 1999;Vannucchi et al., 2006). Zeolites, mostly occurring in veins, are prevalent, but clay minerals, chlorite, epidote, calcite, hematite and pyrite are also common both in veins and replacing phenocrystals, groundmass and mineral grains in the sediments. This mineralogical association defines a metamorphic environment with a maximum temperature of ~250°C. This temperature is further confirmed by the twin set types in the calcite crystals (Meschede et al., 1999). The mélange matrix also contains smectites; the presence of smectite helps to attribute the lowgrade metamorphism to a pre-subduction hydrothermal ocean-floor alteration. In fact, since the onset of illitization and/or chloritization of smectite during shallow subduction occurs at 60°C and in general continues to temperatures as high as 150°C (Moore and Saffer, 2001;Saffer et al., 2008;Środoń, 1999), prograde metamorphism during subduction to the prehite/pumpellyite facies is incompatible with its presence. Based on the relative abundance of the different lithological components the San Pedrillo Unit has been subdivided in packages by Clarke et al (2018). Although the deformation style of the San Pedrillo Unit does not change throughout the different packages, the samples and the figures presented in this paper are coming from the ~1km-thick Punta Marenco Package, where basaltic blocks are embedded in the volcanoclastic matrix. This is a somewhat simple system within the melange when compared to the other packages. The volcanoclastic matrix is mostly composed of clays, rounded silt-sized pyroxene and plagioclase grains, and basalt lithic clasts (SM Figure 4). Sparse microfossils, mostly radiolarians, are also present. Folded veinlets of zeolites and calcite are widespread. From XRD analysis of the sample of volcanoclastic matrix tested in the triaxial experiments, the matrix contains Ca-plagioclase and variably altered clinopyroxene, kaliophilite and low-temperature hydrous zeolite minerals such as analcime, thomsonite and laumontite, chlorite, smectite, and celadonite (SM Figure 5). This mineralogical assemblage is similar to the bulk composition of the basalt sample, even though an increased amount of quartz (SM Figure 5) agrees with some recrystallized radiolarians observed in thin section. This result further confirms that this sediment is directly derived from the erosion of similar basalt (Clarke et al., 2018).

Exhumation of the Osa Melange
A complete analysis of the forearc deformation responsible for the exhumation of the Osa Melange is given in Sak et al. (2004), Vannucchi et al. (2006), and Morell et al. (2019). All authors agree that the post-subduction deformation of the Osa Melange is characterised by steeply dipping to subvertical brittle fractures and faults that cut through the matrix and the blocks. These fractures and faults are related to vertical tectonism inferred to be induced by the subduction of bathymetric relief on the downgoing plate.

Supplementary Numerical Experiments
In the main text we discuss the results and implications of a suite of numerical experiments in which the blocks in a shear channel were idealized as a set of five alternating en-echelon elliptical bodies. After some experimentation, the idealizations in these experiments were chosen to allow us to isolate the origins of observed mechanical behaviour. Here we present and discuss a further suite of experiments that were performed to further test that our findings are not the byproduct of our intentionally simplified experimental configuration. The experiments shown here focus on assessing the degree that observed strong-block-in-weak-matrix behaviour and weak-block-in-strong-matrix behaviour vary with rheological and geometric parameter variations, and with the volume fraction of block material within the shear channel.
Supplementary Figure 6 shows four additional experiments on configurations with high viscosity (>=1e19 Pa-s) competent (cohesion=20 MPa) blocks in a lower viscosity, equally competent matrix.
(Supplement Table 1 defines the sometimes contrasting geological and engineering continuum mechanics terminology used to describe rheological properties.) Panels A-B show the shear-stress (A) and ongoing plastic failure(B) of a similar but more complex scenario than that analyzed in the  Clarke et al. (2018). In this case, the thinnest parts of some blocks (and one large block corner-tip) fail under the ambient channel stresses associated with a 10 18 Pa-s channel viscosity. When failure occurs, it also takes place at isolated discrete locations, which would not correspond to tremor sources with sizes characteristic of the size of the larger blocks.  Clarke et al. (2018). Once again, larger blocks fail in through-going regions of failure. More complex behaviour (e.g. stress-shadowing which 'protects' some blocks from reaching their failure stress) is also seen. main text. The material properties are the same as in the primary experiments, but here the five strong blocks have small random perturbations to their orientations, while being surrounded by a suite of quasi-randomly distributed smaller blocks with the same overall preferred orientation and identical material properties. Block material fills 34% of the channel. In this case, channel shear stresses are slightly more elevated (due to the higher material fraction of more viscous block material), while continuing to exhibit factor-of-two stress concentrations in blocks, in particular within the larger blocks (panel A). No blocks fail (panel B) -the key behaviour noted in the main text. Note that a visually identical stress pattern will be seen for any block viscosity >1e19 Pa-se.g. the channel stress distribution is insensitive to block viscosity as long as it is at least an order of magnitude greater than the matrix viscosity. In these experiments, the matrix between two adjacent blocks often has a higher-than-average stress as it resists being squeezed out from between the two blocks. This behaviour is well-captured by the Lagrangian deformation approximation used here, but is not captured by improperly resolved particle-in-cell treatments of block and matrix rheology, a numerical algorithm that has been commonly applied in related numerical modelling (cf. Beall et al., 2019). Panels C and D show an example with an even higher overall block fraction of 44%. In this case, a few of the thinnest blocks fail under the higher channel stresses induced by the greater block fraction. In general, the first blocks to fail in this and a suite of similar random blob experiments are the thinnest, most elongated blocks, suggesting that failure is shaped by flexural stresses in the blocks. (This is a useful topic for future study). Note that the larger blocks in panel D do not fail, only small thin blocks that are in general close to either the channel walls or to large blocks. This failure pattern would not lead to tremor sources with sizes characteristic of the larger blocks. In panels E and F the matrix viscosity is reduced by a factor of two in comparison to the other examples in this figure, to 5x10 17 Pa-s. In this case, channel and block stresses are correspondingly reduced, and no blocks fail. Finally, panels G and H show an example based on the geometry mapped by Clarke et al. (2018). In this case, the thinnest parts of some blocks, and one corner of a larger more equant block, do fail under the ambient channel stresses associated with a 10 18 Pa-s shear channel viscosity. When failure occurs, it takes place at isolated point-like locations, which would not correspond to tremor sources with sizes characteristic of the size of the larger blocks, as is inferred from seismic observations. These examples corroborate this paper's finding that competent high-viscosity blocks in a shear channel will not produce the failure patterns characteristic of observed seismic tremor.

Supplementary Material Figure 7. Shear channel with high viscosity(>=10 19 Pa-s) but less competent (cohesion=5 MPa) blocks embedded in a lower viscosity (1e18 Pa-s), higher competency (cohesion = 20MPa) matrix. Each pair of panels shows the shear stress field and places where blocks are failing for a range of block-size distributions. Panels (A,B)block fraction = 34% and block viscosity = 10 20 Pa-s. As in the previous examples, the channel stress distribution is insensitive to block viscosity as long as it is at least an order of magnitude greater than the matrix viscosity. Once stresses in a block
Supplementary Figure 7 shows the behaviour of the same examples shown in the previous figure for the case where the block-cohesion is reduced to 5 MPa, e.g. with the same mechanical weakness of blocks relative to matrix as that explored in the examples discussed in the main text. In all examples (Panels 7B,D,F,H) large volumes of the blocks fail plastically, with implied stress drops and failure regions characteristic of seismically observed tremor. Even when the matrix viscosity is reduced to 5x10 17 Pa-s (Panel 7F), the large blocks still fail in through-going regions. Thinner, more lathe-like blocks fail more easily than thicker blocks. Blocks typically fail after less than 5-10 years of shearloading (not shown here, we chose to show the same 65.25 year timestep for all model runs). Other phenomena are also evident. For example, sometimes blocks will experience lower stresses and less failure due to stress 'shadowing' by adjacent blocks (see panel B and panel H in particular). These additional experiments lend further support to the paper's finding that weak low-cohesion blocks can produce failure patterns characteristic of observed seismic tremor.